Coots are aggressive birds, even towards their offspring. Adults have been seen to shake chicks to death, and this may be related to the parents actively adjusting the family size to the feeding possibilities. There are other aspects to this, so please read the article here.

I have seen this on wildlife films. The theory is that if there are too many chicks for the available food the parents attack the weaker chicks (or maybe the one that bothers them the most?) instead of feeding them. The poor chick eventually gives up begging for food and dies of starvation; but the stronger ones survive and get enough food. Which they might not if the parents spread the available food around the whole lot. It's like a form of "family planning" I suppose, but distressing to see.

Does anyone know if parent coots still attack their young if there is plenty of food for all? This would be evidence if the theory is correct or not. Or maybe the chicks' noisy pestering gets on the parents' nerves???

With some other birds, such as hawks and owls, the parents begin brooding the first egg at once, instead of waiting until the clutch is complete. This means that the oldest chick is the largest and strongest and gets more food than the others (and maybe the older ones actively bully the youngest as well). In good years the parents may rear the whole clutch, because the smallest survive until they are big enough to defend themselves; but if food is short or one or more chicks die of other causes the parents still have "insurance" in the surviving young.

Yes, according to Cramp/Simmons(ed) The Birds of the Western Palearctic vol II:

"When a chick attempts to feed from other adults in divided broods, often subject to attack by that parent: head seized between mandibles and whole body shaken for up to 15 s; This may be a mechanism whereby chicks learn which parent intends to feed them (J A Horsfall)."

I've photographed this adult-attacking-chick behaviour with a family of Coots on a small lake in southern France where this was certainly the only Coot family "in town". So, whilst it may also occur when a chick is an interloper, it certainly does happen to an adult's own chick. In my case, there were seven chicks in the brood. It was in a year (2010) when natural food may have been a little lower than previous years, though.